<html>
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
    <title>colcomp</title>
  </head>
  <body bgcolor="#FFFFFF">
    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>colcomp</b> -  column compression, kernel, nullspace</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[W,rk]=colcomp(A [,flag] [,tol])  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>A</b>
        </tt>: real or complex matrix</li>
      <li>
        <tt>
          <b>flag</b>
        </tt>: character string</li>
      <li>
        <tt>
          <b>tol</b>
        </tt>: real number</li>
      <li>
        <tt>
          <b>W</b>
        </tt>: square non-singular matrix (change of basis)</li>
      <li>
        <tt>
          <b>rk</b>
        </tt>: integer (rank of <tt>
          <b>A</b>
        </tt>)</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    Column compression of <tt>
        <b>A</b>
      </tt>: <tt>
        <b>Ac = A*W</b>
      </tt> is 
    column compressed i.e</p>
    <p>
      <tt>
        <b>Ac=[0,Af]</b>
      </tt> with <tt>
        <b>Af</b>
      </tt> full column rank, 
    rank(<tt>
        <b>Af</b>
      </tt>) = rank(<tt>
        <b>A</b>
      </tt>) = <tt>
        <b>rk</b>
      </tt>.</p>
    <p>
      <tt>
        <b>flag</b>
      </tt> and <tt>
        <b>tol</b>
      </tt> are optional parameters: <tt>
        <b>flag = 'qr'</b>
      </tt> 
    or <tt>
        <b>'svd'</b>
      </tt> (default is <tt>
        <b>'svd'</b>
      </tt>).</p>
    <p>
      <tt>
        <b>tol</b>
      </tt> = tolerance parameter (of order <tt>
        <b>%eps</b>
      </tt> as default value).</p>
    <p>
    The <tt>
        <b>ma-rk</b>
      </tt> first columns of <tt>
        <b>W</b>
      </tt> span the kernel of <tt>
        <b>A</b>
      </tt> 
    when <tt>
        <b>size(A)=(na,ma)</b>
      </tt>
    </p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

A=rand(5,2)*rand(2,5);
[X,r]=colcomp(A);
norm(A*X(:,1:$-r),1)
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="rowcomp.htm">
        <tt>
          <b>rowcomp</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="fullrf.htm">
        <tt>
          <b>fullrf</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="fullrfk.htm">
        <tt>
          <b>fullrfk</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="kernel.htm">
        <tt>
          <b>kernel</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p>F.D.;   </p>
  </body>
</html>
